MATH& 163 Calculus III

• Use appropriate convergence tests to discuss the behavior of infinite series
• Compute the Maclaurin and Taylor series expansions of basic and transcendental functions, and use them to solve relevant applications
• Define vector-valued functions, and identify their key characteristics and graphs
• Evaluate and interpret algebraic and calculus operations on vector functions and functions of two or more variables graphically, numerically, and analytically
• Describe curves in planes and space using polar, parametric, and vector-valued forms, and identify situations where these alternate coordinate systems can simplify calculations
• Calculate a path of motion, and describe its curvature, arc length, velocity, and acceleration
• Differentiate and integrate parametric equations, polar equations, and vector-valued functions
• Use double integrals in multiple coordinate systems, and apply principles to finding centers of mass and moments of inertia, volumes of solids, and other applications
• Calculate partial derivatives for functions of several variables, using the chain rule as necessary, and use them to solve relevant applications
• Use mathematical critical thinking skills, problem solving, pattern recognition, and substitution, following structural rules and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation